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Basic Algebra

Twenty questions on algebra

Identify the letter of the choice that best completes the statement or answers the question. ____ 1. Round off 345.0149 to three decimal places. a. 345.015 b. 345.01 c. 345 d. None of the above For questions 2 through 5 use the following values of X: 1, 7, 0, 8 and -6 ____ 2. ∑Χ a. 28 b. 10 c. 22 d

Nilpotents and Zero Divisors

Let x be a nilpotent element of the commutative ring R i.e. x^m for some positive integer m a) Prove that x is either zero or a zero divisor b)Prove that rx is nilpotent for all r in R c)Prove that 1+x is a unit in R d)Deduce that the sum of a nilpotent element and a unit is a unit

Using formula to solve algebra

1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any 2 terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? d)

Parallel RC Circuit Problem (Transfer Function)

See attached file for full problem description. a. Derive the expression for the transfer function of the circuit above. Simplify the expression as far as possible but do not attempt to rationalize it. Refer to the two reactances as Xc1 & Xc2. b. Using the transfer function obtained in part (a) above, derive an expression

Solving systems of equations by substitution and addition

-3/x+2 * 5x+10/9 ax+am+3x+3m/a^2-9 / 2x+2m/a-3 solve and write the answer in the lowest term: 5a^2b/12a * 2a^3b/15ab^6 solve the equation x/x-1-3/x=1/2 solve for y: 2(b+y)=b solve by substitution y=3x+11 2x+3y=0 x+2y=1 8x+6y=4 solve by addition -3x+y=3 2x-3y=5 solve by addition:

Factoring Equations Root Properties

A^2- 6a +9=0 Use the even -root property to solve each question x^2= 9/4 (x-3)^2=16 (w-3/2)^2=7/4 (w+2/3)^2=5/9 Find the perfect square trinomial whose first two terms are given. w^2-5w p^2+6/5p factor each perfect square trinomial. y^2-5y+25/4 t^2+3/5t+9/100 solve by complteing the square

Simplifying Expressions : Rules of Exponents

(3^-6)^1/3 simplify each expression assume the variables represent any real #s and use absolute value as necessary (y^3)^1/3 Simplify assume all variables represent positive #s write answer with positive exponents only w^1/3 / w^3 Simplify each expression right your answer with positive exponents assume that all

Nilpotents, Ideals and Nilradicals

Prove that if R is commutative ring and N=(a1,a2,..am) where each ai is a nilpotent element, then N is a nilpotent ideal, i.e N^n=0 for some positive integer n. Deduce that if the nilradical of R is finitely generated then it is a nilpotent ideal. P.S. the set of nilpotent elements form an ideal which is called nilradical of

Coefficients of Quadratic Equations

Quadratic Equations Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as: 1. Integers 2. Rational numbers 3. Irrational numbers See attached file for full problem description.

Tangent Lines and Logarithmic / Exponential Functions

Tangent Line and Logarithmic/Exponential Functions This project is going to consider the relationship between a point (a, b) on the natural logarithmic and exponential functions and its relationship to the intercept of the tangent line to the respective functions at the point (a, b). Hint: Recall the distance between two

Equations for time and rate problems and their solutions

52. How can a graph be used to determine how many solutions an equation has? 8. Bobbi picks 1 qt in 20 minutes. Blanche picks 1 qt in 25 minutes. How long would it take them to pick one quart if they work together? 14. The speed of a freight train is 15 mph slower than the speed of a passenger train. The freight train tr

Determining formula values.

1) An open-top box is to be constructed from a 4 by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. Answer: b) Graph this fu

Solve: Simplifying Expressions

Simplify the following. Make sure to show all the steps involved. Expression: (3t^2 - 8t +3) + (-5t^2 + 4) - (t^2 + 5t - 3)

Algebra Word Problems

The payment sugar beet growers receive is based on the sucrose content of their delivered beets. A sample is taken from each load of beets and the sugar content in the beets is determined by polarimetry of the beet extract. In a typical situation 50 grams of pulverized beet tissue is homogenized with 360 mL of dilute aluminum

Conservation: Estimating the Size of a Bear Population

Question: To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?

Matrix Algebra with Regression Estimation

Consider the linear regression model Yi = BXi+ Ui where B= Beta i = 1,2 .....5 Xi = 2i Yi = [1 2 3 3 4 ] ' (i.e a 5x1 vector) and Sigma ^2 = 1 Compute the OLS Estimate of B . Can you work it out slowly, step by step, as I am having a hard time doing the problems in the book, and need a sample to look back at.

Solving Inequalities Word Problems

How do you solve the inequality (x + 1)(x - 6) < 0, and express the solution using interval notation. If an object is shot upward with an initial velocity of 240 feet per second so that its height s (in feet) above the ground after t seconds is given by s = -16t2 + 240t. For what values of t will the object be at least 416 f

Simplifying Expressions

Three problems: 3/2w + 7/2w a+7 9-5a ______ + _______ a-4 a-4 4h-3 h-6 ______ - ______ h(h+1) H(h+1)

What if an equation had three variables?

What if an equation had three variables? You now have practice solving equations with one and equations with two variables. Compare equations with one variable to equations with two variables. How are they different?

Quadratic Equations

1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the

Solving Applied Problems: Algebra

Please solve the following problems: 1. The St. Mark's Community Barbecue served 250 dinners. A child's plate cost $3.50 and an adult's plate cost $7.00. A total of $1347.50 was collected. How many of each type of plate was served. 2. Deep Thought Granola is 25% nuts and dried fruit. Oat Dream Granola is 10% nuts and